The angular velocity of a flywheel with radius 1.0 m varies according to ω(t)=2.0t Plot ac(t)andat(t)ac(t)andat(t) from t=0 to 3.0 st=0 to 3.0 s for r=1.0mr=1.0m. Analyze these results to explain when ac≫atac≫at and when ac≪atac≪at for a point on the flywheel at a radius of 1.0 m.
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- The angle through which a rotating wheel has turned in time t is given by q = t3-12t2+36t+30, where q is in radians and t is seconds. What is the average angular velocity between t = 2.0 s and 6.0 s The instantaneous angular velocity w at t = 6.0 s The average angular acceleration α between t = 2.0 s and t = 6.0 s When is the instantaneous angular acceleration zero?Tab sLk A printing press has a roller 17 inches in diameter. A point on the roller's surface moves at a speed of 85 feet per second. What is the roller's angular speed? The roller's angular speed is radians per second. (Round your answer to the nearest hundredth.) Esc I 1 Q A 91°F Sunny 261 N @ 2 W S Alt X 3E D C STR 4 F C FS do 5 % T V OL G 6 B F7 H W & 7 P U N J 8 +00 8 F9 1 k M F10 ( 9 K O V LO F11 O L P All + 99+ F12 . V PMULTIPLE CHOICE Question 3 Convert 260° to radians. A 4.5 rad B 260 rad C 1.4 rad 820 rad D. All Changes Saved 2 of 11 Total Questions Answered rse Stude... 回 V 8
- Four particles, A, B, C, and D, are rotating around their individual axes of rotation with different distances from the axis and different angular velocities. Which one of the particles has the smallest angular velocity, given the distance R and the linear velocity v? VA = 5.0 m/s, RA = 2.0 m VB = 2.0 m/s, Rg = 0.5 m vc= 3.0 m/s, RC = 3.0 m VD = 1.0 m/s, RD = 0.2 mA ceiling fan with 89-cmcm-diameter blades is turning at 70 rpmrpm . Suppose the fan coasts to a stop 30 ss after being turned off What is the speed of the tip of a blade 10 ss after the fan is turned off?The answer is supposed to be v=2.56m/s but I'm not sure how to write out the problem.
- A ring of radius R is released from rest to roll down a rough incline (assuming there's no energy loss due to friction and there's no slipping in the rolling). Calculate its speed when it reaches the foot of the incline, 4R below the starting point. 4R R (KE+KE,+PE), = = (KE+KE,+PE)f 1 2 0+0+mg4R = ¹1 mv³² + ¹² (mR²³)w² +0 2 2 RSolution (a) Find the angular displacement after 2.00 s, in both radians and revolutions. 1 A0 = w;t + Use Equation 7.8, setting @; 1.60 rad/s, a = 3.50 rad/s2, and t = 2.00 s. 1 Að = (1.60 rad/s) (2.00 s) + (3.50 rad/s²) (2.00 s)² 2 A0 = 10.2 rad Convert radians to revolutions. A0 = (Am rad)(1.00 rev/2r rad) AO = 16.02 X rev Your response differs from the correct answer by more than 100%. (b) What is the angular speed of the wheel at t = 2.00 s? Substitute the same values into Equation 7.7. @ = @; + at = 1.60 rad/s + (3.50 rad/s²)(2.00 s) W = rad/s Remarks The result of part (b) could also be obtained from Equation 7.9 and the results from part (a). - INThe angular position of a rod varies as 20.0t2 radians from time t = 0 . The rod has two beads on it as shown in the following figure, one at 10 cm from the rotation axis and the other at 20 cm from the rotation axis. (a) What is the instantaneous angular velocity of the rod at t = 5 s? (b) What is the angular acceleration of the rod? (c) What are the tangential speeds of the beads at t = 5 s? (d) What are the tangential accelerations of the beads at t = 5 s? (e) What are the centripetal accelerations of the beads at t = 5 s?
- A solid 0.6350 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.6350 m. What minimum translational speed ?min must the ball have when it is a height ?=0.9944 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?. Use ?=9.810 m/s^2 for the acceleration due to gravity.Point A of the circular disk is at the angular position 0 = 0 at time t = 0. The disk has angular velocity wo = 0.29 rad/s at t = 0 and subsequently experiences an angular acceleration a = 1.8t where t is in seconds, and a is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 2.7 s. Assumer = 145 mm. α Answers: VA = aд = 90 (i ( i 0 6.806 i + i + i i 1 0.705 j) m/s j) m/s²16-21. The motor turns the disk with an angular velocity of w = (5P + 3t) rad/s, where t is in seconds. Determine the magnitudes of the velocity and the n and t components of acceleration of the point A on the disk when t = 3 s. 150 mm